SpecialFuncs::Besk Function

Overload List

#	Signature	Description
1	TCplx Besk(double NU, TCplx Z);	Modified Bessel function of the second kind, complex argument: K_(nu)(z).
2	TSCplx Besk(float NU, TSCplx Z);
3	TCplx Besk(double NU, double A);	Modified Bessel function of the second kind, real argument: K_(nu)(x).
4	TSCplx Besk(float NU, float A);
5	TCplx Besk(double NU, TCplx Z, bool Scale);	Modified Bessel function of the second kind, complex argument, optional scaling: K_(nu)(z).
6	TSCplx Besk(float NU, TSCplx Z, bool Scale);
7	TCplx Besk(double NU, double A, bool Scale);	Modified Bessel function of the second kind, real argument, optional scaling: K_(nu)(x).
8	TSCplx Besk(float NU, float A, bool Scale);
9	void Besk(double NU, TCplx Z, TVec resCY, bool* Scale);	Sequence of modified Bessel functions of the second kind, complex argument: K_(nu+i)(z), i=0... N-1.

Overload 1: TCplx Besk(double NU, TCplx Z);

Modified Bessel function of the second kind, complex argument: K_(nu)(z).

#	Name	Type	Description
1	NU	double	Defines the order of Hankel function.
2	Z	TCplx	Defines complex value for which Kn(Z) should be evaluated.

Returns: K_(nu)(z), the modified Bessel function of the second kind (Macdonald function) of order NU at Z.

Remarks:

K_(nu) is the decaying solution of the modified Bessel equation; it satisfies K_(-nu)(z)=K_(nu)(z) and K_(nu)(z) = pi/2 (I_(-nu)(z)-I_(nu)(z))/sin(nupi). Domain. Any finite complex Z with z != 0; the principal branch is used. Behavior. At
z=0 the function diverges and the implementation returns +inf in both components.

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler

Overload 2: TSCplx Besk(float NU, TSCplx Z);

#	Name	Type	Description
1	NU	float
2	Z	TSCplx

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler

Overload 3: TCplx Besk(double NU, double A);

Modified Bessel function of the second kind, real argument: K_(nu)(x).

#	Name	Type	Description
1	NU	double	Defines the order of Hankel function.
2	A	double	Defines real value for which Kn(A) should be evaluated.

Returns: K_(nu)(x) of order NU at the real argument A (returned as a TCplx).

Remarks:

K_(-nu)(x)=K_(nu)(x). Domain. A>0 (real). Behavior. K diverges at x=0, where the implementation returns +inf.

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler

Overload 4: TSCplx Besk(float NU, float A);

#	Name	Type	Description
1	NU	float
2	A	float

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler

Overload 5: TCplx Besk(double NU, TCplx Z, bool Scale);

Modified Bessel function of the second kind, complex argument, optional scaling: K_(nu)(z).

#	Name	Type	Description
1	NU	double	Defines the order of the Bessel function of the second kind Kn.
2	Z	TCplx	Defines complex value for which Kn(Z) should be evaluated.
3	Scale	bool	If Scale parameter is true, Kn(Z) is multiplied by e^z.

Returns: K_(nu)(z) of order NU. When is true the result is multiplied by e^z, i.e. e^z K_(nu)(z), which removes the exponential decay for large Re z.

Remarks:

K_(nu)(z) = pi/2 (I_(-nu)(z)-I_(nu)(z))/sin(nupi), K_(-nu)(z)=K_(nu)(z).

Domain. Any finite complex Z with z != 0. Behavior. Returns +inf at z=0.

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler

Overload 6: TSCplx Besk(float NU, TSCplx Z, bool Scale);

#	Name	Type
1	NU	float
2	Z	TSCplx
3	Scale	bool

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler

Overload 7: TCplx Besk(double NU, double A, bool Scale);

Modified Bessel function of the second kind, real argument, optional scaling: K_(nu)(x).

#	Name	Type	Description
1	NU	double	Defines the order of the Bessel function of the second kind Kn.
2	A	double	Defines real value for which Kn(A) should be evaluated.
3	Scale	bool	If Scale parameter is true, Kn(A) is multiplied by e^x.

Returns: K_(nu)(x) of order NU; when is true it is multiplied by e^x.

Remarks:

Domain. A>0 (real). Behavior. Returns +inf at x=0.

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler

Overload 8: TSCplx Besk(float NU, float A, bool Scale);

#	Name	Type
1	NU	float
2	A	float
3	Scale	bool

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler

Overload 9: void Besk(double NU, TCplx Z, TVec *resCY, bool Scale);

Sequence of modified Bessel functions of the second kind, complex argument: K_(nu+i)(z), i=0... N-1.

#	Name	Type	Description
1	NU	double	Defines the order of Hankel function.
2	Z	TCplx	Defines complex value for which Kn((Z) should be evaluated.
3	resCY	TVec *	Contains result on output and needs to be sized to desired N on input. The result holds: cyRes[i] = K(NU + i, Z)*Exp(Z) when scaled and cyRes[i] = K(NU + i, Z) when not scaled.
4	Scale	bool	If Scale parameter is true, Kn(A) is multiplied by e^z.

Returns: Fills with K_(nu+i)(z) for i=0,...,N-1 (N = input length of ). When is true each element is multiplied by e^z.

Remarks:

resCY[i] = e^z K_(nu+i)(z), i=0,...,N-1, with the factor applied only when scaling is enabled. Domain. resCY must be a non-empty complex double vector; at z=0 every element is set to +inf.

Declared in Dew::Math::Units::SpecialFuncs · Dew.Math/Units.SpecialFuncs.h · Cross-compiler